RETURN TO BIG APPLE? Carl Pavano, who was a bust with the Yankees, is on the Mets’ radar, according to multiple industry sources. Photo: Anthony J. Causi

Could The American Idle book a return engagement to the Big Apple — only this time in Flushing?

According to multiple industry sources, the Mets have reached out to the representative for Carl Pavano, dubbed “American Idle” by The Post during the right-hander’s Yankees years, as one of many lines cast in an effort to re-stock their starting rotation following R.A. Dickey’s trade to Toronto.

In fact, Pavano isn’t even the only member of the 2012 Twins who sits on the Mets’ radar. The club also has reached out to left-hander Francisco Liriano and many of the other remaining free-agent pitchers, including 2011 and 2012 Met Chris Young and Shaun Marcum, who spent the last two seasons with Milwaukee.

The Mets also have engaged in trade discussions with the Dodgers, who have former Met Chris Capuano and Aaron Harang, neither of whom likely would be in the team’s starting rotation if the 2013 season began today.

The spot likely will not be filled until after the new year, as the baseball market typically slows down around the holidays.

Pavano, who turns 37 next month, is coming off an injury-shortened 2012 season with the Twins in which he posted a 6.00 ERA over 11 starts, totaling 63 innings. He suffered what was called a bone bruise on his right humerus bone and made his last appearance of the season on June 1.

He is believed to be healthy now, and even last year, he exhibited his trademark strong control — 33 strikeouts and eight walks — that makes him appealing to clubs looking for pitching.

What remains to be seen is whether Pavano actually would come back to New York, given how disastrous his 2005-08 stay with the Yankees went. The Yankees and Pavano actually talked about a second act when Pavano was a free agent two years ago, yet Pavano held serious reservations about it, and ultimately the Twins gave him a two-year package to trump the Yankees’ interest in a one-year arrangement.

Liriano, 29, put together a 5.34 ERA in 156 2/3 combined innings with the Twins and White Sox, striking out 167 and walking 87. He has a friendship with the Mets’ Johan Santana, as Liriano shined in his rookie season with Minnesota, 2006 when Santana won his second American League Cy Young Award. Though the Mets like Young, based on the way he pitched for them the past two seasons, they’re seeing if they can find someone with a higher upside. Marcum, 31, could prove too pricey for the Mets, who have about $10 million to spend, but the Mets would be interested if his market fell. The right-hander recorded a 3.70 ERA for the Brewers in 124 innings (21 starts) in 2012, missing about two months with a right elbow injury.

Capuano, 34, put together a solid 2012 campaign for the Dodgers, tallying a 3.72 ERA in 198 1/3 innings pitched (33 starts). He will make $6 million next season and has a mutual $6 million option for 2014 with a $1 million buyout. Harang, also 34, compiled a 3.61 ERA in 179 2/3 innings pitched (31 starts) this past season and is due $7 million in 2013, with a 2014 mutual option for between $7 million and $8 million (depending on his innings pitched this coming year) against a $2 million buyout. The Dodgers, having added Zack Greinke and Hyun-Jin Ryu to their starting rotation, figure to move at least one of Capuano and Harang.

The Mets continue to search for another righty-hitting outfielder, preferably one who plays right field so they can shift Lucas Duda to left. The two most obvious options are free agents Scott Hairston and Cody Ross, both of whom are generating considerable interest in the market and seem likely to get two-year deals. Hairston, 32, has spent the last two seasons with the Mets.